1. INTRODUCTION

Astronomy and physics bring different perspectives to the
``cosmological constant problem.'' Originally introduced by Einstein as
a new term in his gravitational field equations [and later regretted
by him as ``the biggest blunder of my life'' (quoted in
Gamow 1970)],
the cosmological constant, ,
confronts observational astronomers as a
possible additional term in the equation that, according to general
relativity, governs the expansion factor of the universe R(t),

1.

Here M is
the mass density; k = - 1, 0, + 1 for a Universe that is
respectively open, ``flat,'' and closed; and H is the Hubble constant,
whose observable value at the present epoch t0 is
denoted H0.

Equation 1 says that three competing terms drive the universal
expansion: a matter term, a cosmological constant term, and a
curvature term. It is convenient to assign symbols to their respective
fractional contributions at the present epoch. We define

2.

where zero subscripts refer to the present epoch. Equation 1 then
implies

3.

it is also sometimes convenient to define
tot =
M +
= 1 -
k. It is
an observational question whether a non-zero
is required to achieve
consistency in Equation 3. This is the astronomer's cosmological
constant problem.

The Heisenberg uncertainty principle allows particle-antiparticle
pairs spontaneously to appear and disappear. The theoretical particle
physicist thus sees the term
in Equation 3 as an inevitable
concomitant to the M
term. As M is
associated with a density of real
particles, so is associated with virtual,
``vacuum'' states of those
same particles' species - that is, with the energy-momentum density of
their vacuum states. The gravitational effect of these virtual
particles gives the vacuum an energy density
vac
(Zel'dovich 1967).
Although particle physicists do not know how to compute
vac exactly,
theory allows one to estimate its value. Unfortunately, the estimates
disagree with observational limits by a factor of 10120. This is the
physicist's cosmological constant problem.

In this review, we sample both the astronomer's and the physicist's
viewpoints. The differing perspectives lead to different perceived
goals. An epochal astronomical discovery would be to establish by
convincing observation that
is non-zero. An important physics
discovery, on the other hand, would be to adduce a convincing
theoretical model that requires
to be exactly zero.

In comparison with H0 and
M, attempts to
measure have been
infrequent and modest in scope. Moreover, in many respects, the
physical signatures of are
smaller and more subtle than those of
the other two parameters, at least from an observational
perspective. These considerations should severely limit our
expectations for current observational information concerning
.

Table 1 lists five fiducial cosmological models,
parametrized by M
and , which we will refer to in
following sections as Models A
through E. They represent extreme, though not impossible, limits on
the present state of knowledge. In fact, we will see that
distinguishing among these models, and thus among variations in
Equation 3 having dominant versus negligible
terms, is quite
challenging at present.